It could be random, or selectable, but also pre-created by the game with a bit of lore.
What was the ship's mission before it crashed determining your team.
A scientific purposed mission: top farmer, top researcher, low builder/miner (these three also have medium doctor status)and a low guard/hunter
A prisoner transfer: top guard/hunter, medium builder/miner, medium farmer/butcher and one prisoner
A military ship: top guard/hunter, top builder/miner, low farmer/butcher, low researcher
These are just examples. Obviously these would also have secondary skills that i can't get into at the moment but if it's a good suggestion then i can expand ( however i am leaving today for a job far away and i don't know if i'll have any time in the next 6 months). An example would be that in the military ship scenario you get an officer (no need to add this as a trait, just as lore) who is a good hunter/builder/farmer (survival skills) and a medium(or low) doctor (first aid skills). However the rest of the team's skills would suffer.
Also, you could get an interesting intro scenario of what the mission was all about and the names of the people. This way you get attached to your team before you even begin to play. You could even design the entire crew and then get a random four people (one in each perspective field) that survived from that particular crew - although that's a bit of a longshot.
Other missions could be
Construction ship, Trade ship, Exploration ship, or digging deeper a research ship whose mission was to research and explore a Transcendent world. Space pirates, tribals that were slaves in a slaveship and ended up surviving the crash, anything goes.
Some other aspects would be to add where do these come from to determine certain perks (like starting resources or researches), so for example if it comes from a glitterworld then they should start with some perks of that world.
However one of these scenarios should be the scenario as it is now. The default one. Maybe a "cruise ship" which was supposed to be for vacations, so you get random people.
The good thing about these scenarios is that you will be able to provide a predetermined experience to the player, while leaving the choice to him. Also, there is nothing that needs to be added apart from text and creating characters according to each scenario. Obviously there would be some need for balancing (maybe one mission is too hard, another is too easy), however nothing new is being added code-wise.
This could later on affect the ending, each scenario could have its own, maybe the military group has to bring its mission to completion, maybe the war is over until that point.
Also, some scenarios could be unlockable by certain events. So for example, as one stated in some endings/triggers he wrote about, if you get everyone united under a cyber-hive mind, then you can unlock a team that comes from a transcendent world (how cool would that be) but again, that's for later on.
To sum up: My cheap idea is to implement the ship's original mission which determines what your team will be, while keeping the default option of the team being random (or "rolled" let's say).
